Certain bibasic hypergeometric transformations and their applications (Q1919600)

Bailey's transformation [\textit{L.J. Slater}, Generalized hypergeometric functions (1966; Zbl 0135.28101), p. 58], based effecively upon the elementary manipulation of series [compare \textit{H. M. Srivastava} and \textit{H. L. Manocha}, A treatise on generating functions (1984; Zbl 0535.33001), p. 100] is very fruitful. In the present context it is used to deduce interesting transformation formulae involving bibasic \(q\)-functions by applying known summation formulae and transformations of basic hypergeometric functions. A number of the more interesting expressions given as special cases of the main results do not involve independent bases.